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Experimental study on the influences of grain boundary scattering on the charge and heat transport in gold and platinum nanofilms

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Abstract

The electrical and thermal conductivities of polycrystalline gold and platinum nanofilms have been measured simultaneously using a direct current heating method from 60 to 300 K. The measured electrical and thermal conductivities are greatly decreased from the corresponding bulk values. And it is found that the reduction increases as the temperature decreases. The deviation from the bulk value is due to the effect of grain boundary scattering. Furthermore, the experimental results indicate that the grain boundary scattering effect imposes greater influence to the charge transport than to the heat transport. Consequentially, the Lorentz number is several times larger than that of bulk materials, leading to the violation of the Wiedemann–Franz law. The reflection coefficient R (0.86 in platinum, 0.42 in gold) at grain boundaries is obtained based on the Mayadas-Shatzkes theory and Matthiessen’s rule, which agrees well with the previous experiments.

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Abbreviations

C v :

Specific heat of heat (J Kg−1 K−1)

d :

Mean diameter of grains (m)

e :

Elementary charge (C)

k B :

Boltzmann constant (J K−1)

l b :

Mean free path of bulk material (m)

L b :

Lorenz number of bulk material (WΩ K−2)

m :

Electron mass (Kg)

n :

Electron density (m−3)

R :

Reflection coefficient at grain boundaries

T :

Temperature (K)

v F :

Fermi velocity (ms−1)

α = l b R/d(1 − R):

Combined parameter in MS law

ζ c :

Constant Lorentz number (WΩ K−2)

θ :

Debye temperature (K)

λ rel :

Relative thermal conductivity

λ f :

Thermal conductivity of nanofilm (Wm−1 K−1)

λ b :

Thermal conductivity of bulk material (Wm−1 K−1)

ρ :

Electrical resistivity (Ωm)

ρ 0 :

Zero-point electrical resistivity (Ωm)

ρ ee :

Electron–electron scattering term (Ωm K−2)

ρ sd :

Inter-band electron scattering term (Ωm K−3)

ρ ss :

Intra-band electron scattering term (Ωm K−5)

σ rel :

Relative electrical conductivity

σ f :

Electrical conductivity of nanofilm (Ω−1 m−1)

σ b :

Electrical conductivity of bulk material (Ω−1 m−1)

τ :

Relaxation time (s)

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Acknowledgments

This project was supported by National Natural Science Foundation of China (Grant Nos. 51076080, 50730006 and 50976053).

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Authors and Affiliations

  1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Hai-Dong Wang, Jin-Hui Liu, Xing Zhang & Zeng-Yuan Guo

  2. Graduate School of Engineering, Kyushu University, Fukuoka, 819-0395, Japan

    Koji Takahashi

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  1. Hai-Dong Wang
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  2. Jin-Hui Liu
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  3. Xing Zhang
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  4. Zeng-Yuan Guo
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  5. Koji Takahashi
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Corresponding author

Correspondence to Xing Zhang.

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Dedicated to Prof. Dr.-Ing. Dr.-Ing. E.h. Mult. Franz Mayinger on the occasion of his 80th bithday.

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Wang, HD., Liu, JH., Zhang, X. et al. Experimental study on the influences of grain boundary scattering on the charge and heat transport in gold and platinum nanofilms. Heat Mass Transfer 47, 893–898 (2011). https://doi.org/10.1007/s00231-011-0825-5

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  • DOI: https://doi.org/10.1007/s00231-011-0825-5

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